• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.613-629
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• 2021

In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on τ-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1361-1378
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• 2008

This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.1-12
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• 2015

This paper is concerned with boundary value problems for systems of n-th order dynamic equations on time scales. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.399-410
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• 2019

In the manuscript, we concern with the existence of solutions of boundary value problems for fourth order nonlinear discrete systems. Some criteria for the existence of at least one nontrivial solution of the problem are obtained. The proof is mainly based upon the variational method and critical point theory. An example is presented to illustrate the main result.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.187-220
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• 2016

This paper is concerned with a kind of non-homogeneous boundary value problems for singular second order differential systems with Laplacian operators. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of boundary value problems are established. An example is presented to illustrate the main results.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.665-685
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• 2000

The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems ($\Phi$($\upsilon$'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T], $\Phi$: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where $\Phi$(u) is the vector p-Laplacian $\mid$u$\mid$p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.891-909
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• 2022

The main objective of this paper is to develop a concrete inverse formula of the system induced by the fourth-order finite difference method for two-point boundary value problems with Robin boundary conditions. This inverse formula facilitates to make a fast algorithm for solving the problems. Our numerical results show the efficiency and accuracy of the proposed method, which is implemented by the Thomas algorithm.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.711-721
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• 2010

Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.